Answer:
[tex]x = -4\\x = -3\\x = 3[/tex]
Step-by-step explanation:
To find the real zeros you must match the function to zero and factor the expression.
We have a polynomial of degree 3.
We try to group the terms to perform the factorization
[tex]x ^ 3 + 4x ^ 2-9x-36 = 0\\\\x ^ 2(x + 4) - 9(x + 4) = 0[/tex]
Now we take (x + 4) as a common factor
[tex](x + 4)(x ^ 2 -9) = 0[/tex]
If we have an expression of the form [tex](a ^ 2-b ^ 2)[/tex] we know that this expression is equivalent to:
[tex](a ^ 2-b ^ 2) = (a + b)(a-b)[/tex]
In this case
[tex]a = x\\b = 3[/tex]
So:
[tex](x ^ 2 -9) = (x + 3)(x-3)[/tex]
Finally:
[tex]x ^ 3 + 4x ^ 2-9x-36 = (x + 4)(x + 3)(x-3) = 0[/tex]
The solutions are:
[tex]x = -4\\x = -3\\x = 3[/tex]
